Analytic approximations to Kelvin functions with applications to electromagnetics

We present analytical approximations for the real Kelvin function ber(x) and the imaginary Kelvin function bei(x), using the two-point quasifractional approximation procedure. We have applied these approximations to the calculation of the current distribution within a cylindrical conductor. Our approximations are simple and accurate. The infinite number of roots is also obtained with the approximation and the precision increases with the value of the root. Our results could find useful applications in problems where analytical approximations of the Kelvin functions are needed.Comment: J. Phys. A (in press). 11 pages, 3 figure

Computation of the electron beam quality kQ,Q0k_{{\rm Q,Q}_0} factors for the NE2571, NE2571A and NE2581A thimble ionization chambers using PENELOPE

The quality correction factor $k_{Q,Q_{0}}$ for electron beams was calculated for three thimble ionization chambers, namely, NE2571, NE2571A and NE2581A. The Monte Carlo code PENELOPE was used to estimate the overall correction factor $f_{\rm c,Q}$ of these chambers for electron beams with nominal energies ranging between 6 and 22 MeV, corresponding to a Varian Clinac 2100 C/D. A $^{60}$Co beam was used as reference quality ${\rm Q}_0$. Also eight monoenergetic electron beams reproducing the quality index $R_{50}$ of the Clinac beams were considered. The $k_{Q,Q_{0}}$ factors were calculated as the ratio between $f_{\rm c,Q}$ and $f_{{\rm c,Q}_0}$. Those obtained for the NE2571 ionization chamber show a nice agreement with those calculated by Muir and Rogers with EGSnrc. As it occurred to other ionization chambers analyzed in previous works, the $k_{{\rm Q,Q}_0}$ factors found for the monoenergetic beams are larger (smaller) than those corresponding to the Clinac beams at low (high) $R_{50}$ values, the differences being slightly above $0.5\%$. Finally, the $k_{{\rm Q,Q}_0}$ factors obtained in the case of the NE2571A chamber are systematically ~0.5% below those of its predecessor chamber, the NE2571.Comment: 8 pages, 2 figures, 3 table

Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo

Improvements beyond the primitive approximation in the path integral Monte Carlo method are explored both in a model problem and in real systems. Two different strategies are studied: the Richardson extrapolation on top of the path integral Monte Carlo data and the Takahashi-Imada action. The Richardson extrapolation, mainly combined with the primitive action, always reduces the number-of-beads dependence, helps in determining the approach to the dominant power law behavior, and all without additional computational cost. The Takahashi-Imada action has been tested in two hard-core interacting quantum liquids at low temperature. The results obtained show that the fourth-order behavior near the asymptote is conserved, and that the use of this improved action reduces the computing time with respect to the primitive approximation.Comment: 19 pages, RevTex, to appear in J. Chem. Phy

A geometrical model for the Monte Carlo simulation of the TrueBeam linac

Monte Carlo (MC) simulation of linacs depends on the accurate geometrical description of the head. The geometry of the Varian TrueBeam (TB) linac is not available to researchers. Instead, the company distributes phase-space files (PSFs) of the flattening-filter-free (FFF) beams tallied upstream the jaws. Yet, MC simulations based on third party tallied PSFs are subject to limitations. We present an experimentally-based geometry developed for the simulation of the FFF beams of the TB linac. The upper part of the TB linac was modeled modifying the Clinac 2100 geometry. The most important modification is the replacement of the standard flattening filters by ad hoc thin filters which were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6MV and 10MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements for radiation fields ranging from 3X3 to 40X40 cm2. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were done for dose profiles obtained from MC simulations using the second generation of PSFs distributed by Varian for the TB linac. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TB PSFs for all fields considered, except for the 40X40 cm2 field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach makes possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties by employing different MC codes

Quantum Monte Carlo Algorithm Based on Two-Body Density Functional Theory for Fermionic Many-Body Systems: Application to 3He

We construct a quantum Monte Carlo algorithm for interacting fermions using the two-body density as the fundamental quantity. The central idea is mapping the interacting fermionic system onto an auxiliary system of interacting bosons. The correction term is approximated using correlated wave functions for the interacting system, resulting in an effective potential that represents the nodal surface. We calculate the properties of 3He and find good agreement with experiment and with other theoretical work. In particular, our results for the total energy agree well with other calculations where the same approximations were implemented but the standard quantum Monte Carlo algorithm was usedComment: 4 pages, 3 figures, 1 tabl